Problem 3. (Continuity /Differentiability /Product rule) Consider the following function: (We can change the function to x2sin(In(x2) if we have an issue with the absolute value, and the parts below still work). x2 sin(In(x2) ) if x * 0 f (x) = 0 if x = 0 a. Show that f(x) is continuous everywhere. b. Find f'(x) for x * 0. c. Show that f(x) is differentiable at x = 0